In the related art, for example, as disclosed in Japanese Unexamined Patent Publication No. 2010-287162, an apparatus is known, which detects another vehicle travelling in front of a host vehicle, detects an operation of the host vehicle overtaking another vehicle, and determines whether or not the overtaking operation is appropriate based on a positional relationship with respect to a lane in which the host vehicle travels during the overtaking operation. This apparatus determines whether the overtaking operation of the host vehicle is appropriate and performs a driving evaluation of the host vehicle.
Incidentally, in performing a travel control on a vehicle, performing a control of overtaking a preceding vehicle can be considered. In this case, the overtaking control is performed by detecting a travelling state of the preceding vehicle. However, in a case where the preceding vehicle accelerates after starting the overtaking operation, there is a problem in that it is not possible to appropriately overtake the preceding vehicle. For this reason, in a case where the preceding vehicle accelerates, it is considered that the overtaking control is stopped.